Which equation describes the relation indicated by the table? x = -2,0,4,6 y = 3,2,0, -1

- (1/2)x + 2

Solution:

1) Table

x    y

-2   3
0    2
4    0
6   -1

The first thing that you must probe is whether the relation is linear.

When the relation is linear the rate of change is constant.

The rate of change is Δy / Δx

2) Let's calculate that rate for all the points given:

x    y

-2   3
0    2 ---> Δx = 0 -(-2) = 2, Δy = 2 - 3 = - 1 => Δy / Δx = - 1/2
4    0 ---> Δx = 4 - 0 =4, Δy = 0 - 2 = -2 => Δy / Δx = -2/4 = - 1/2
6   -1 ---> Δx = 6 - 4 = 2, Δy = - 1 - 0 = -1 => Δy / Δx = - 1/2

So, we have shown that the relation is linear.

3) Now, you can use the equation of the line: y = mx + b, where m is the slope (rate of change Δy / Δx) and b is the y-intercept.

We already found m = -1/2

The y-intercept is the value of y when x = 0, which you can get from the table; b = 2.

Therefore the equation is: y = (-1/2)x + 2.

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